Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities
From MaRDI portal
Publication:2184729
DOI10.1007/s00211-020-01113-3OpenAlexW3014280493MaRDI QIDQ2184729
Publication date: 29 May 2020
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-020-01113-3
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Best approximation, Chebyshev systems (41A50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)
Related Items
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation, Pointwise error estimates and local superconvergence of Jacobi expansions, Analysis of Error Localization of Chebyshev Spectral Approximations, Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: effects of different bases, Comparisons of best approximations with Chebyshev expansions for functions with logarithmic endpoint singularities, On optimal convergence rates of Laguerre polynomial expansions for piecewise functions, New error bounds for Legendre approximations of differentiable functions, An efficient quadrature rule for weakly and strongly singular integrals, How much faster does the best polynomial approximation converge than Legendre projection?, Convergence Rates on Spectral Orthogonal Projection Approximation for Functions of Algebraic and Logarithmatic Regularities
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The relationships between Chebyshev, Legendre and Jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions
- On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities
- Error bounds for approximation in Chebyshev points
- On the decay rate of Chebyshev coefficients
- Inequalities for Jacobi polynomials
- Numerical analysis of a fast integration method for highly oscillatory functions
- On the optimal convergence rates of Chebyshev interpolations for functions of limited regularity
- On Van der Corput-type lemmas for Bessel and Airy transforms and applications
- Estimating the derivative of the Legendre polynomial
- A new and sharper bound for Legendre expansion of differentiable functions
- On the Optimal Estimates and Comparison of Gegenbauer Expansion Coefficients
- Sharp Error Bounds for Jacobi Expansions and Gegenbauer--Gauss Quadrature of Analytic Functions
- On Error Bounds for Orthogonal Polynomial Expansions and Gauss-Type Quadrature
- Spectral Methods
- Asymptotic Representations of Fourier Integrals and the Method of Stationary Phase
- Asymptotic Expansions of Fourier Integrals Involving Logarithmic Singularities
- Spectral Methods for Time-Dependent Problems
- The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points
- Spectral Methods in MATLAB
- A Practical Guide to Pseudospectral Methods
- On exponential convergence of Gegenbauer interpolation and spectral differentiation
- Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces
- Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
- On the convergence rates of Legendre approximation
- Is Gauss Quadrature Better than Clenshaw–Curtis?
- On the Convergence of the Chebyshev Series for Functions Possessing a Singularity in the Range of Representation
- Coefficients in Series Expansions for Certain Classes of Functions
- The Evaluation and Estimation of the Coefficients in the Chebyshev Series Expansion of a Function
- On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity
